Abstract

In this paper, we considered the laminar fully developed flow, of a Newtonian fluid, inducts of rectangular cross-section. Poisson’s partial differential equation Saint-Venant solution was used, to calculate Poiseuille number values whatever is rectangles aspect ratio. From these results, we considered limit cases of square duct and plane Poiseuille flow (infinite parallel plates). We showed there exists a rectangle equivalent to a circular cross-section for energy dissipation through viscous friction. Finally, we gave some mathematical consequences of this approach for odd integers zeta function calculations and Catalan’s constant.

Keywords

rectangular ducts, poisson’s equation, saint-venant solution, viscous friction, zeta function, catalan’s constant, circular cross-section, laminar flow, rheological equation, integral mean value, euler-riemann zeta, poiseuille flow, geometrical shapes, mechanical energy, newtonian liquid